1. Field of the Invention
The present invention relates to a flow meter, and more particularly, to meter electronics and methods for geometric thermal compensation in a flow meter.
2. Statement of the Problem
Vibrating conduit sensors, such as Coriolis flow meters and vibrating densitometers, typically operate by detecting motion of a vibrating conduit that contains a flowing material. Properties associated with the material in the conduit, such as mass flow, density and the like, can be determined by processing measurement signals received from motion transducers associated with the conduit. The vibration modes of the vibrating material-filled system generally are affected by the combined mass, stiffness and damping characteristics of the containing conduit and the material contained therein.
A typical Coriolis flow meter includes one or more flow conduits or flow tubes that are connected inline in a pipeline or other transport system and convey material, e.g., fluids, slurries and the like, in the system. Each conduit may be viewed as having a set of natural vibration modes including, for example, simple bending, torsional, radial, and coupled modes. In a typical Coriolis flow measurement application, a conduit is excited in one or more vibration modes as a material flows through the conduit, and motion of the conduit is measured at points spaced along the conduit. Excitation is typically provided by an actuator, e.g., an electromechanical device, such as a voice coil-type driver, that perturbs the conduit in a periodic fashion. Mass flow rate may be determined by measuring time delay or phase differences between motions at the transducer locations. Two such transducers (or pickoff sensors) are typically employed in order to measure a vibrational response of the flow conduit or conduits, and are typically located at positions upstream and downstream of the actuator. The two pickoff sensors are connected to electronic instrumentation by cabling, such as two independent pairs of wires. The instrumentation receives signals from the two pickoff sensors and processes the signals in order to derive a mass flow rate measurement.
For a set of conditions of the flow meter, (e.g., for a particular temperature, mount, external loads, etc.) the mass flow rate is linearly proportional to the time delay (Δt) between the pickoff sensors. This relationship is given in equation 1 below.{dot over (m)}=FCF·(Δt−zero)  (1)The FCF term is a proportionality constant and is commonly referred to as the flow calibration factor. The zero value is an empirically derived zero flow offset.
The FCF is primarily dependent upon the stiffness and the geometry of the flow conduits of the flow meter. The geometry includes features such as the locations where the two phase or time measurements are made. The stiffness is dependent on the flow conduit's material properties as well as on the geometry of the conduits. For a particular flow meter, the FCF value and the zero value are found through a calibration process performed with a calibration fluid flowing at two known mass flow rates and at a specific calibration temperature.
If the stiffness or geometry of the flow meter changes during operation, after the time of initial calibration, then the FCF will also change. For example, an increase in the operating temperature to a level above the calibration temperature may result in a change in the stiffness of the flow meter. To ensure accurate mass flow measurement requires that the FCF value and the zero value remain nearly constant. This may be very difficult to achieve. Alternatively, an accurate mass flow measurement requires that a robust method of accounting for changes in the FCF and/or zero values is employed.
The prior art flow meter is typically calibrated at a specific reference temperature (T0). However, in use the flow meter is often operated at temperatures that are different than the reference temperature.
In the prior art, a flow meter is compensated for changes in temperature in a relatively simple manner. It is known in the prior art that the modulus of elasticity changes with temperature. As a result, in the prior art the mass flow and density equations have been augmented to account for this effect on the modulus of elasticity.
The typical form of the prior art mass flow equation, including temperature compensation for the modulus of elasticity (E) or Young's modulus, is given in equation 2 below.{dot over (m)}=FCF·(1−φ·ΔT)·(Δt−zero)  (2)The Young's modulus term (1−φ·ΔT) defines how the FCF changes corresponding to a change in flowmeter temperature from the reference temperature (T0).
The slope of the above function, φ, often referred to as FT, is typically determined through experimentation for a particular flow meter design or flow meter family. In the prior art, it is commonly believed that FT is essentially the same as the slope of the modulus of elasticity with temperature.
However, the modulus of elasticity is not always linear over the full range of temperatures which a flow meter is operated. To account for this non-linearity, higher order polynomials have been employed to better compensate for this change, such as equation 3 below.{dot over (m)}=FCF(1−φ1·ΔT−φ2·ΔT2−φ3·ΔT3−φ4·ΔT4)·(Δt−zero)  (3)The higher order polynomial (1−φ1·ΔT−φ2·ΔT2 . . . ) term defines how the FCF changes with a change in flowmeter temperature. The Young's modulus term is represented as TFy. The (TFy) term can comprise a first order linear term or can comprise a polynomial.
A Coriolis flow meter can also measure the density (ρf) of a process fluid within the vibrating frame of reference. The period of vibration, squared, is linearly proportional to the mass of the vibrating system divided by its stiffness. For a particular condition of the flow conduits, the stiffness and mass are constant and the fluid density (ρf) is linearly proportional to the period squared. This relationship is given in equation 4 below.ρf=C1·K2−C2  (4)The C1 term is a proportionality constant and the C2 term is an offset. The coefficients C1 and C2 are dependent on the stiffness of the flow conduits and on the mass and the volume of fluid within the flow meter. The coefficients C1 and C2 are determined by calibrating the flow meter using two fluids of known density.
In the prior art, the density computation has also been compensated for temperature. The typical form of the density equation, including temperature compensation for the modulus of elasticity, is given in equation 5 below.ρf=C1·K2·(TFy)−C2  (5)The (TFy) term defines how the tube period squared changes with a change in temperature from the reference temperature (T0), as previously discussed.
The slope of the above function, φ, often referred to as DT in this equation, is typically determined through experimentation for a particular flow meter design or flow meter family. It should be noted that as in the mass flow rate, higher order functions can be used for refining the effect of temperature on the density temperature compensation process. Like FT, in the prior art it is commonly believed that DT is the same as the slope of modulus of elasticity with temperature. As a result, in the prior art, the mass flow rate and the density are temperature compensated in an identical fashion.
At about the reference (i.e., calibration) temperature, the DT and FT temperature compensation procedures function acceptably well. However, their inherent inaccuracy/incompleteness becomes noticeable and pronounced at extremes of temperature. For this reason, additional compensation/calibration processes are often necessary in the prior art. For example, for flow meters destined for use at high temperatures, such as 90 degrees C., for example, a new calibration process is performed at a similarly high reference temperature. This additional calibration process may guarantee that the flow meter operate within desired accuracy at temperatures around this new calibration temperature. However, if the ambient temperature significantly drops (or rises), the accuracy of the flowmeter is still adversely affected.